Nuprl Lemma : has-value-monotonic
∀[a,b:Base]. ((b)↓) supposing ((a ≤ b) and (a)↓)
Proof
Definitions occuring in Statement :
has-value: (a)↓,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
base: Base,
sqle: s ≤ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
has-value: (a)↓,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas referenced :
is-exception_wf,
cbv-sqequal0,
sqle_trans,
base_wf,
has-value_wf_base,
sqle_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
axiomSqleEquality,
hypothesis,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
baseClosed,
baseApply,
closedConclusion,
independent_functionElimination,
divergentSqle,
sqleRule,
independent_isectElimination
Latex:
\mforall{}[a,b:Base]. ((b)\mdownarrow{}) supposing ((a \mleq{} b) and (a)\mdownarrow{})
Date html generated:
2016_05_13-PM-03_46_24
Last ObjectModification:
2016_01_14-PM-07_11_10
Theory : call!by!value_2
Home
Index